Least Common Multiple (LCM) of 115 and 179
The least common multiple (LCM) of 115 and 179 is 20585.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 115 and 179?
First, calculate the GCD of 115 and 179 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 179 = 0 remainder 115 |
| 2 | 179 ÷ 115 = 1 remainder 64 |
| 3 | 115 ÷ 64 = 1 remainder 51 |
| 4 | 64 ÷ 51 = 1 remainder 13 |
| 5 | 51 ÷ 13 = 3 remainder 12 |
| 6 | 13 ÷ 12 = 1 remainder 1 |
| 7 | 12 ÷ 1 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 126 and 178 | 11214 |
| 57 and 71 | 4047 |
| 99 and 131 | 12969 |
| 188 and 122 | 11468 |
| 58 and 191 | 11078 |